Global Surgery Formula for the Casson-Walker Invariant
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3-manifold
A01=Christine Lescop
Addition
Alexander polynomial
Ambient isotopy
Author_Christine Lescop
Betti number
Casson invariant
Category=PBK
Category=PBM
Category=PBP
Change of basis
Change of variables
Cobordism
Coefficient
Combination
Combinatorics
Computation
Conjugacy class
Connected component (graph theory)
Connected space
Connected sum
Cup product
Determinant
Diagram (category theory)
Disk (mathematics)
Empty set
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exterior (topology)
Fiber bundle
Fibration
Function (mathematics)
Fundamental group
Homeomorphism
Homology (mathematics)
Homology sphere
Homotopy sphere
Indeterminate (variable)
Integer
Klein bottle
Knot theory
Manifold
Morphism
Notation
Orientability
Permutation
Polynomial
Prime number
Projective plane
Scientific notation
Seifert surface
Sequence
Summation
Symmetrization
Taylor series
Theorem
Topology
Tubular neighborhood
Unlink
Product details
- ISBN 9780691021324
- Weight: 227g
- Dimensions: 197 x 254mm
- Publication Date: 11 Jan 1996
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.
Christine Lescop is Researcher in Mathematics at the Centre National de la Recherche Scientifique at the Institut Fourier in Grenoble, France.
